Tangent Line Equation Calculator
Find the equation of the tangent line to f(x) = axⁿ at any point x₀.
Returns the slope, y-intercept, and full equation in slope-intercept and point-slope form.
The tangent line to a curve at a point touches the curve at exactly that point and has the same slope as the curve there. The slope at any point is the derivative.
For f(x) = a * x^n, the derivative is f’(x) = n * a * x^(n-1).
At the point x0, the slope of the tangent is m = f’(x0) = n * a * x0^(n-1). The point of tangency is (x0, f(x0)).
Point-slope form: y - f(x0) = m * (x - x0) Slope-intercept form: y = m * x + (f(x0) - m * x0)
The y-intercept is b = f(x0) - m * x0.
One thing students often confuse: the tangent line is a global linear function, not just a local approximation. It extends to the full plane as a straight line. The fact that it matches the curve at x0 (same position and same slope) is what makes it “tangent.” For higher derivatives, you can build a Taylor polynomial that also matches curvature – but the tangent line only matches to first order.
The tangent line is also the best linear approximation to f near x0. If you need to estimate f(x0 + small delta) without computing f directly, the tangent gives: f(x0 + delta) ≈ f(x0) + f’(x0) * delta. This is linear approximation, widely used in engineering and physics.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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